A clump of weeds which are thriving in a shaded area next-door are
trying unsuccessfully to invade my garden under a gravel board and I am
trying to identify it.

It has long runners which travel about 3" underground and it throws up
an abundance of about 2' long, mostly single, stems, the first few
inches of which are purple. The remainder of the stem is green

Nearly all of the foliage is at the tip of the plant and it is quite
similar to a slim version of curly parsley.

Any ides please?

Thanks,
Emrys Davies.